A Study for the Improvement of the Vibration and Acceleration Measurement

The calibration of vibration and acceleration pick-ups (hereinafter pick-ups) has become increasingly important due to the growing needs for accurate measurements of vibration and acceleration. To date, there is no official standard for calibration of the pick-ups in the middle to high vibration frequency rage (80 Hz ~ 5 kHz) in Japan. Thus the reliability of the vibration and acceleration measurement has not been legally established. In this study, the calibration system for the pick-ups is developed, and the technical infrastructure for calibration has been established. A novel silicon resonant type acceleration pick-up is also proposed to reduce the phase shift error in vibration measurements. This report proceeds as follows. In Chapter 1, an introduction is given, where the background and the purpose of the study are described. In Chapter 2, the sine-approximation method (SAM), which is described in the updated International Standard Organization (ISO 16063-11), is applied. Calibration equipment, which uses a modified Michelson-type laser interferometer, mathematical algorithms are developed and described. A regression analysis method is applied for data transforming and uncertainty evaluation. A new simple algorithm for phase unwrapping in the SAM is also proposed. In Chapter 3, uncertainty sources and their contribution are examined. The pick-ups can be calibrated within the frequency range from 20 Hz to 5 kHz by the developed calibration system. Expanded measurement uncertainties of about 0.1 to 2 % (with a 95% confidence level) is obtained. The conventional calibration methods, the fringe counting method (FCM) and the minimum point method (MPM), are also applied and compared in each calibration region and uncertainty. The advantage of the SAM and problems with the system are also discussed. In Chapter 4, the phase shift evaluation results of three types (piezoelectric-type, servo-type and capacitance-type) of commercially available vibration and acceleration pickups are presented. The evaluations were performed using the SAM. A regression analysis is also successfully applied for uncertainty evaluation in phase calculation. Expanded uncertainties of less than ±6×10rad in phase shift evaluation at 5 kHz has been obtained. Three piezoelectric type pickups manufactured by different makers are also evaluated and compared. We observed phase shift differences of up to 4×10rad in each sensor. In Chapter 5, a silicon resonant type acceleration pick-up is proposed and demonstrated. As the preliminary study, a resonator which is fabricated by silicon micro-machining technique is evaluated. The resonator vibrated in torsional mode and has two degrees of freedoms to improve its Q value. Resonant vibration frequency and Q values of the silicon resonator are examined. The acceleration pick-up consists of torsional resonators and proof mass. The induced acceleration causes inertial force on proof mass, then the resonant frequency of the resonators are changed by the effect of inertial force, thus the phase shift of the output is expected to be minimal. The fabricated silicon resonant type pick-up shows the resonant frequency change of 0.03 % for the input static acceleration level of 19.6 m/s. In Chapter 6, a multiple path differential laser interferometer is developed to realize a high resolution of motion. The optical and electric design is reported and discussed. The developed laser interferometer realizes a resolution of 25 nm, where the previous one is 50 nm. By employing newly developed laser interferometer, the calibration system becomes robust against the outer vibration noise. Thus, the technical subjects for the calibration of the pick-ups in the middle to high vibration frequency rage (80 Hz ~ 5 kHz) are solved. In Chapter 7, conclusions are given.